Torus Planet page 2

Recently, because of appearance the torussians inside sql-ex.ru site, much information about Lorus Galaxy became known. It turned out that Torus 36x36 is not biggest planet of the system. In the aims of cultural exchange some facts of historic chronicles of Torus was added to common and checking site databases (Painting, Ships, etc.).

The sql-ex task situations explains that Torus unit of length is called a torometer, and united currency is torobucks. The Torus life base is water and its ice variety. Task situation contains other information on physical-chemical characteristics, economical, social and political systems of planets Torus MxN.

Now we will not be tied with our “common” databases and present the next “universal” task situation on Torus.

Neighbor states on Torus 3x7

For each state of the Torus 3x7:

T00   T01   …   T06
T10   T11   …   T16
T20   T21   …   T26
find a list of neighbor states, which have bounds of not non-zero length. Result must be outputted in the table with five columns: [State], [NN], [WW], [SS], [EE].

Hint. This is the answer for common (non-toroidal) case:

State	NN	WW	SS	EE
T00	NULL	NULL	T10	T01
T01	NULL	T00	T11	T02
T02	NULL	T01	T12	T03
T03	NULL	T02	T13	T04
T04	NULL	T03	T14	T05
T05	NULL	T04	T15	T06
T06	NULL	T05	T16	NULL
T10	T00	NULL	T20	T11
T11	T01	T10	T21	T12
T12	T02	T11	T22	T13
T13	T03	T12	T23	T14
T14	T04	T13	T24	T15
T15	T05	T14	T25	T16
T16	T06	T15	T26	NULL
T20	T10	NULL	NULL	T21
T21	T11	T20	NULL	T22
T22	T12	T21	NULL	T23
T23	T13	T22	NULL	T24
T24	T14	T23	NULL	T25
T25	T15	T24	NULL	T26
T26	T16	T25	NULL	NULL

This is solution for toroidal case:

Console

Execute

SELECT
 'T'+CAST(i  AS varchar)+CAST(j  AS varchar) [State]
,'T'+CAST(k1 AS varchar)+CAST(j1 AS varchar) [NN]
,'T'+CAST(i2 AS varchar)+CAST(k2 AS varchar) [WW]
,'T'+CAST(k4 AS varchar)+CAST(j4 AS varchar) [SS]
,'T'+CAST(i3 AS varchar)+CAST(k3 AS varchar) [EE]
FROM (SELECT j=0 UNION ALL SELECT 1 UNION ALL SELECT 2 UNION ALL SELECT 3 UNION ALL 
         SELECT 4 UNION ALL SELECT 5 UNION ALL SELECT 6)J
CROSS JOIN (SELECT i=0 UNION ALL SELECT 1 UNION ALL SELECT 2)I
CROSS APPLY(SELECT i1=i-1,j1=j,i2=i,j2=j-1,i3=i,j3=j+1,i4=i+1,j4=j)D
CROSS APPLY(SELECT
 k1=CASE WHEN i1<0 THEN 2 ELSE i1 END
,k2=CASE WHEN j2<0 THEN 6 ELSE j2 END
,k3=CASE WHEN j3>6 THEN 0 ELSE j3 END
,k4=CASE WHEN i4>2 THEN 0 ELSE i4 END
)E;

Valid answer:

State	NN	WW	SS	EE
T00	T20	T06	T10	T01
T01	T21	T00	T11	T02
T02	T22	T01	T12	T03
T03	T23	T02	T13	T04
T04	T24	T03	T14	T05
T05	T25	T04	T15	T06
T06	T26	T05	T16	T00
T10	T00	T16	T20	T11
T11	T01	T10	T21	T12
T12	T02	T11	T22	T13
T13	T03	T12	T23	T14
T14	T04	T13	T24	T15
T15	T05	T14	T25	T16
T16	T06	T15	T26	T10
T20	T10	T26	T00	T21
T21	T11	T20	T01	T22
T22	T12	T21	T02	T23
T23	T13	T22	T03	T24
T24	T14	T23	T04	T25
T25	T15	T24	T05	T26
T26	T16	T25	T06	T20

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SQL Problems and solutions

S. I. Moiseenko

Appendixes

Appendix 3. Chronicles of Torus

Torus Planet page 2

Neighbor states on Torus 3x7